NONEQUILATERAL HEXAGONAL PATTERNS

Rotational symmetry of pattern formation problems is the origin of a v ariety of patterns (rolls, squares, hexagons etc.) in convection and r eaction-diffusion systems. Traditionally, only the patterns based on e quilateral lattices in the Fourier space were considered. In the prese nt paper, we develop an analysis of the patterns with slightly differe nt lengths of the basic wave vectors. The analysis applies as well to systems with a broken rotational symmetry (convection in an inclined l ayer, etc.). We find, in the framework of the amplitude equations, exi stence and stability conditions for periodic nonequilateral patterns b ased on two and three wave vectors. In the latter case, special attent ion is paid to the case when the three amplitudes are coupled by the r esonant interaction.